Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
# maa chudaaye duniya
from math import sqrt, ceil

def findnumber(arr, z, lo, hi):
    while hi >= lo:
        mid = lo + ((hi-lo)//2)
        if arr[mid] == z:
            return True
        elif z > arr[mid]:
            lo = mid + 1
        else:
            hi = mid - 1
    return False
             
n=int(input())*2
z = ceil(sqrt(n))
arr = [i*(i+1) for i in range(1, z)]
fnd = False
for i in arr:
    to_find = n - i
    if findnumber(arr, to_find, 0, len(arr) - 1):
        print('YES')
        fnd = True
        break
if not fnd:
    print('NO')